Solving and Learning Nonlinear PDEs with Gaussian Processes

24 March 2021

Papers citing "Solving and Learning Nonlinear PDEs with Gaussian Processes"

50 / 76 papers shown

Title
Solving Nonlinear PDEs with Sparse Radial Basis Function Networks Zihan Shao Konstantin Pieper Xiaochuan Tian 31 0 0 12 May 2025
Gaussian Process Policy Iteration with Additive Schwarz Acceleration for Forward and Inverse HJB and Mean Field Game Problems Xianjin Yang Jingguo Zhang 24 0 0 01 May 2025
Towards scientific machine learning for granular material simulations -- challenges and opportunities Marc Fransen Andreas Fürst D. Tunuguntla Daniel N. Wilke Benedikt Alkin ... Takayuki Shuku WaiChing Sun T. Weinhart Dongwei Ye Hongyang Cheng AI4CE 39 1 0 01 Apr 2025
Flexible and Efficient Probabilistic PDE Solvers through Gaussian Markov Random Fields Tim Weiland Marvin Pfortner Philipp Hennig AI4CE 47 0 0 11 Mar 2025
Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis Yasamin Jalalian Juan Felipe Osorio Ramirez Alexander W. Hsu Bamdad Hosseini H. Owhadi 48 0 0 02 Mar 2025
Understanding Generalization in Physics Informed Models through Affine Variety Dimensions Takeshi Koshizuka Issei Sato AI4CE 112 0 0 31 Jan 2025
Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operator Jonghyeon Lee B. Hamzi Boya Hou H. Owhadi G. Santin Umesh Vaidya 82 1 0 21 Dec 2024
Toward Efficient Kernel-Based Solvers for Nonlinear PDEs Zhitong Xu Da Long Yiming Xu Guang Yang Shandian Zhe Houman Owhadi 40 0 0 15 Oct 2024
Physics-informed kernel learning Nathan Doumèche Francis Bach Gérard Biau Claire Boyer PINN 39 2 0 20 Sep 2024
Stability Analysis of Physics-Informed Neural Networks for Stiff Linear Differential Equations Gianluca Fabiani Erik Bollt Constantinos Siettos A. Yannacopoulos 56 0 0 27 Aug 2024
Kernel Sum of Squares for Data Adapted Kernel Learning of Dynamical Systems from Data: A global optimization approach Daniel Lengyel P. Parpas B. Hamzi H. Owhadi 35 1 0 12 Aug 2024
Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalities José A. Carrillo Yifan Chen Daniel Zhengyu Huang Jiaoyang Huang Dongyi Wei AI4CE 29 3 0 22 Jul 2024
Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Models Kaiyuan Tan Peilun Li Thomas Beckers AI4CE 26 3 0 17 Jun 2024
Linearization Turns Neural Operators into Function-Valued Gaussian Processes Emilia Magnani Marvin Pfortner Tobias Weber Philipp Hennig UQCV 71 1 0 07 Jun 2024
Scaling up Probabilistic PDE Simulators with Structured Volumetric Information Tim Weiland Marvin Pfortner Philipp Hennig AI4CE 42 2 0 07 Jun 2024
Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 65 1 0 21 May 2024
Neural Operator induced Gaussian Process framework for probabilistic solution of parametric partial differential equations Sawan Kumar R. Nayek Souvik Chakraborty 40 2 0 24 Apr 2024
Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning Zongren Zou Tingwei Meng Paula Chen Jérome Darbon George Karniadakis 52 7 0 12 Apr 2024
Label Propagation Training Schemes for Physics-Informed Neural Networks and Gaussian Processes Ming Zhong Dehao Liu Raymundo Arroyave U. Braga-Neto AI4CE SSL 26 1 0 08 Apr 2024
A High Order Solver for Signature Kernels M. Lemercier Terry Lyons 31 3 0 01 Apr 2024
Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems Rafael Anderka M. Deisenroth So Takao 38 1 0 26 Feb 2024
PINN-BO: A Black-box Optimization Algorithm using Physics-Informed Neural Networks Dat Phan-Trong Hung The Tran A. Shilton Sunil R. Gupta 49 0 0 05 Feb 2024
Learning About Structural Errors in Models of Complex Dynamical Systems Jin-Long Wu Matthew E. Levine Tapio Schneider Andrew M. Stuart AI4CE 21 17 0 29 Dec 2023
Gaussian process learning of nonlinear dynamics Dongwei Ye Mengwu Guo 23 4 0 19 Dec 2023
A Kronecker product accelerated efficient sparse Gaussian Process (E-SGP) for flow emulation Yu Duan M. Eaton Michael Bluck 19 0 0 13 Dec 2023
Decoding Mean Field Games from Population and Environment Observations By Gaussian Processes Jinyan Guo Chenchen Mou Xianjin Yang Chao Zhou AI4CE 27 5 0 08 Dec 2023
Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots Théo Bourdais Pau Batlle Xianjin Yang Ricardo Baptista Nicolas Rouquette H. Owhadi 26 0 0 28 Nov 2023
Bridging Algorithmic Information Theory and Machine Learning: A New Approach to Kernel Learning B. Hamzi Marcus Hutter H. Owhadi 26 3 0 21 Nov 2023
Solving High Frequency and Multi-Scale PDEs with Gaussian Processes Shikai Fang Madison Cooley Da Long Shibo Li R. Kirby Shandian Zhe 40 4 0 08 Nov 2023
Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structures Jinchao Feng Charles Kulick Sui Tang 29 2 0 01 Nov 2023
Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels Da Long Wei W. Xing Aditi S. Krishnapriyan R. Kirby Shandian Zhe Michael W. Mahoney 26 0 0 09 Oct 2023
Sampling via Gradient Flows in the Space of Probability Measures Yifan Chen Daniel Zhengyu Huang Jiaoyang Huang Sebastian Reich Andrew M. Stuart 30 13 0 05 Oct 2023
Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points Gianluca Fabiani N. Evangelou Tianqi Cui J. M. Bello-Rivas Cristina P. Martin-Linares Constantinos Siettos Ioannis G. Kevrekidis 40 2 0 25 Sep 2023
Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discovery Pongpisit Thanasutives Takashi Morita M. Numao Ken-ichi Fukui 34 2 0 20 Aug 2023
Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes Yuxiao Wen Eric Vanden-Eijnden Benjamin Peherstorfer 29 13 0 27 Jun 2023
Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysis Kim Jie Koh F. Cirak AI4CE 29 9 0 23 May 2023
A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data Elham Kiyani K. Shukla George Karniadakis M. Karttunen 33 21 0 18 May 2023
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs Pau Batlle Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 34 17 0 08 May 2023
Kernel Methods are Competitive for Operator Learning Pau Batlle Matthieu Darcy Bamdad Hosseini H. Owhadi 16 38 0 26 Apr 2023
Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEs Jinshuai Bai Guirong Liu Ashish Gupta Laith Alzubaidi Xinzhu Feng Yuantong T. Gu PINN 29 1 0 13 Apr 2023
Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes Yifan Chen H. Owhadi F. Schafer 45 31 0 03 Apr 2023
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models Anant Raj Umut Simsekli Alessandro Rudi DiffM 31 1 0 30 Mar 2023
Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance Yifan Chen Daniel Zhengyu Huang Jiaoyang Huang Sebastian Reich Andrew M. Stuart 27 17 0 21 Feb 2023
The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach Yongcun Song Xiaoming Yuan Hangrui Yue PINN 37 0 0 16 Feb 2023
Random Grid Neural Processes for Parametric Partial Differential Equations Arnaud Vadeboncoeur Ieva Kazlauskaite Y. Papandreou F. Cirak Mark Girolami Ömer Deniz Akyildiz AI4CE 35 11 0 26 Jan 2023
Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systems L. Yang Xiuwen Sun B. Hamzi H. Owhadi Nai-ming Xie 24 20 0 24 Jan 2023
Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification A. Alberts Ilias Bilionis 34 12 0 18 Jan 2023
Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients Marc Härkönen Markus Lange-Hegermann Bogdan Raiță 32 15 0 29 Dec 2022
Parameter Inference based on Gaussian Processes Informed by Nonlinear Partial Differential Equations Zhao-Xia Li Shih-Feng Yang Jeff Wu 11 2 0 22 Dec 2022
Sobolev Spaces, Kernels and Discrepancies over Hyperspheres S. Hubbert Emilio Porcu Chris J. Oates Mark Girolami 24 4 0 16 Nov 2022